Determination of the size distribution and specific surface of fine powders by photoextinction methods I. Theoretical estimate of variation in extinction coefficient with particle size using a white light source

Abstract

Determination of the size characteristics of fine powders by measuring the attenuation of a light beam passing through a settling suspension of the particles is, superficially, a most attractive technique. Problems arise due to the breakdown in the laws of geometric optics as the size of the particles approach the wavelength of light, the interaction between the incident radiation and the particles being extremely complex. The net effect is that particles cut off more light than would be expected from their geometrical cross-section. For particle sizes smaller than the wavelength of the incident radiation, light is scattered predominantly backward, the fraction of light scattered in a forward direction increasing with particle size until the scattered light is contained in a small angle cone, and hence picked up by the receiver. The relationship between extinction coefficient K and particle size, where K is equal to the ratio of the light cut off by the particle and the light which would be cut off if the laws of geometric optics held, has been derived theoretically for plane, parallel, monochromatic radiation and small angle of acceptance for spheres and infinitely long cylinders and found to be strongly dependent on the optical properties of the particle and the wavelength of the incident radiation. No such theoretical treatment has yet been applied to the conditions found in photosedimentometers using a white light source. In this paper theoretical curves are developed. These have been tested experimentally using spherical particles and conventional equipment. The result of this work has been the design, construction and testing of a new type of photosedimentometer.